Kermack and McKendrick Models on a Two-Scale Network and Connections to the Boltzmann Equations

Luckhaus, Stephan; Stevens, Angela

Abstract

The Kermack–McKendrick models are often misinterpreted solely as the well-known SIR-ODE-system for the dynamics of susceptibles, infectious and removed during an epidemic. But McKendrick’s equations are by far more general. Here we explain - how his systems can be adapted to cover a small world-large world scenario, where the small world has a different infection mechanism, - how they can be adapted to several variants of viruses competing, and - how even the classical Boltzmann equations can be written in McKendrick form. In the language of delay differential equations, in all three examples the delay parameter becomes multidimensional.